Decide whether each of the following statements makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning
I made a distribution of 15 apartment rents in my neighborhood. One apartment had a much higher rent than all of the others, and this outlier caused the mean rent to be higher than the median rent.
Choose the correct answer below.
A. The statement does not make sense because an outlier with a large value increases the median, but does not affect the mean
B. The statement makes sense because an outlier with a large value increases the mean, but does not affect the median
C. The statement does not make sense because an outlier with a large value increases the mean and the median by the same amount
D. The statement does not make sense because an outlier with a large value decreases the mean, but does not affect the median.
Answer
Final Answer: \(\boxed{\text{B. The statement makes sense because an outlier with a large value increases the mean, but does not affect the median}}\)
Step 1 ：The statement is discussing the effect of an outlier on the mean and median of a data set. The mean is the average of all the values in the data set, so a significantly larger value would increase the mean. The median, on the other hand, is the middle value of a data set when it is ordered from least to greatest. An outlier would not affect the median unless it changes the middle value of the data set.
Step 2 ：Therefore, the statement makes sense because an outlier with a large value increases the mean, but does not affect the median.
Step 3 ：Final Answer: \(\boxed{\text{B. The statement makes sense because an outlier with a large value increases the mean, but does not affect the median}}\)
